A clamping device according to the precharacterizing clause of claim 1 is known, for example, from DE 103 04 640 A1. This clamping device comprises two disc-shaped clamping plate elements between which rolling bodies are guided, with the surface of one of the clamping plate elements having clamping ramps for the rolling bodies. This design of the clamping plate elements causes the axial distance between the clamping plate elements to change when one of the elements is pivoted relative to the other element. The rolling bodies are guided in a guide element which is arranged between the clamping plate elements. The entire clamping device can be installed as a preassembled unit in a motor vehicle.